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A table can have at most one PRIMARY KEY constraint but it can have as many as you want UNIQUE KEY constraints.

Columns that are part of the PRIMARY KEY must be defined as NOT NULL. That is not required for columns that are part of UNIQUE KEY constraints. If the columns are not Nullable, then there is no difference between Unique and Primary Keys.

Another minor difference is that you can choose the name you want for a UNIQUE KEY constraint (and index). On the other hand, the PRIMARY KEY has the default name: PRIMARY.

If you don't explicitly declare a PK in InnoDB tables, it will create one under the covers for you. You cannot access, order, or filter by this implicit key. This has ramifications in terms of resources as each secondary index contains a copy pointer to the PK of the row.